Determine the number of solutions the system has. Then state whether the system of equations is consistent or inconsistent and if it is independent or dependent.y=x−3𝑦=𝑥-3 y=−4x+3𝑦=-4𝑥+3 Multiple choice question.A)1, consistent, independentB)Infinite, consistent, dependentC)1, consistent, dependentD)No solution, inconsistent
Question
Determine the number of solutions the system has. Then state whether the system of equations is consistent or inconsistent and if it is independent or dependent.y=x−3𝑦=𝑥-3 y=−4x+3𝑦=-4𝑥+3 Multiple choice question.A)1, consistent, independentB)Infinite, consistent, dependentC)1, consistent, dependentD)No solution, inconsistent
Solution
To solve this problem, we need to analyze the two equations given:
- y = x - 3
- y = -4x + 3
We can see that the two equations have different slopes. The first equation has a slope of 1, and the second equation has a slope of -4. Since the slopes are not equal, the lines represented by these equations will not be parallel and will intersect at some point. Therefore, the system has one solution.
A system of equations is consistent if it has at least one solution. Since our system has one solution, it is consistent.
A system of equations is independent if it has exactly one solution. Since our system has one solution, it is independent.
So, the answer is A) 1, consistent, independent.
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